scholarly journals An analysis on Quantum mechanical Stability of Regular Polygons on a Point Base Using Heisenberg Uncertainty Principle

2021 ◽  
Vol 9 (10) ◽  
pp. 74-79
Author(s):  
Anurag Chapagain
Keyword(s):  
Quantum Mechanics ◽  
Uncertainty Principle ◽  
Stability Problem ◽  
Classical Mechanics ◽  
Quantum Mechanical ◽  
Heisenberg Uncertainty Principle ◽  
Heisenberg Uncertainty ◽  
Degree Of Stability ◽  
The Stability ◽  
Heisenberg's Uncertainty Principle

Abstract: It is a well-known fact in physics that classical mechanics describes the macro-world, and quantum mechanics describes the atomic and sub-atomic world. However, principles of quantum mechanics, such as Heisenberg’s Uncertainty Principle, can create visible real-life effects. One of the most commonly known of those effects is the stability problem, whereby a one-dimensional point base object in a gravity environment cannot remain stable beyond a time frame. This paper expands the stability question from 1- dimensional rod to 2-dimensional highly symmetrical structures, such as an even-sided polygon. Using principles of classical mechanics, and Heisenberg’s uncertainty principle, a stability equation is derived. The stability problem is discussed both quantitatively as well as qualitatively. Using the graphical analysis of the result, the relation between stability time and the number of sides of polygon is determined. In an environment with gravity forces only existing, it is determined that stability increases with the number of sides of a polygon. Using the equation to find results for circles, it was found that a circle has the highest degree of stability. These results and the numerical calculation can be utilized for architectural purposes and high-precision experiments. The result is also helpful for minimizing the perception that quantum mechanical effects have no visible effects other than in the atomic, and subatomic world. Keywords: Quantum mechanics, Heisenberg Uncertainty principle, degree of stability, polygon, the highest degree of stability

scholarly journals A CLASS OF GUP SOLUTIONS IN DEFORMED QUANTUM MECHANICS

2010 ◽  
Vol 19 (12) ◽  
pp. 2003-2009 ◽  
Author(s):  
POURIA PEDRAM
Keyword(s):  
Black Hole ◽  
Quantum Mechanics ◽  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Loop Quantum Gravity ◽  
Black Hole Physics ◽  
Generalized Uncertainty Principle ◽  
Heisenberg Uncertainty Principle ◽  
Deformed Algebra ◽  
Heisenberg Uncertainty

Various candidates of quantum gravity such as string theory, loop quantum gravity and black hole physics all predict the existence of a minimum observable length which modifies the Heisenberg uncertainty principle to the so-called generalized uncertainty principle (GUP). This approach results from the modification of the commutation relations and changes all Hamiltonians in quantum mechanics. In this paper, we present a class of physically acceptable solutions for a general commutation relation without directly solving the corresponding generalized Schrödinger equations. These solutions satisfy the boundary conditions and exhibit the effect of the deformed algebra on the energy spectrum. We show that this procedure prevents us from doing equivalent but lengthy calculations.

scholarly journals The Heisenberg Uncertainty Principle as an Endogenous Equilibrium Property of Stochastic Optimal Control Systems in Quantum Mechanics

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1533 ◽  
Author(s):  
Jussi Lindgren ◽  
Jukka Liukkonen
Keyword(s):  
Optimal Control ◽  
Quantum Mechanics ◽  
Uncertainty Principle ◽  
Stochastic Optimal Control ◽  
Stochastic Approach ◽  
Heisenberg Uncertainty Principle ◽  
Control Approach ◽  
Heisenberg Uncertainty ◽  
Original Interpretation ◽  
Optimal Control Approach

We provide a natural derivation and interpretation for the uncertainty principle in quantum mechanics from the stochastic optimal control approach. We show that, in particular, the stochastic approach to quantum mechanics allows one to understand the uncertainty principle through the “thermodynamic equilibrium”. A stochastic process with a gradient structure is key in terms of understanding the uncertainty principle and such a framework comes naturally from the stochastic optimal control approach to quantum mechanics. The symmetry of the system is manifested in certain non-vanishing and invariant covariances between the four-position and the four-momentum. In terms of interpretation, the results allow one to understand the uncertainty principle through the lens of scientific realism, in accordance with empirical evidence, contesting the original interpretation given by Heisenberg.

scholarly journals Classical and Quantum Physics in Selected Economic Models

2011 ◽  
Vol 3 (1) ◽  
pp. 7-20 ◽  
Author(s):  
Ewa Drabik
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Financial Markets ◽  
Uncertainty Principle ◽  
Schrodinger Equation ◽  
Quantum Physics ◽  
Economic Models ◽  
Heisenberg Uncertainty Principle ◽  
Wave Particle Duality ◽  
Heisenberg Uncertainty

Classical and Quantum Physics in Selected Economic ModelsA growing number of economic phenomena are nowadays described with methods known in physics. The most frequently applied physical theories by economists are: (1) the universal gravitation law and (2) the first and second law of thermodynamics. Physical principles can also be applied to the theory of financial markets. Financial markets are composed of individual participants who may be seen to interact as particles in a physical system. This approach proposes a financial market model known as a minority game model in which securities and money are allocated on the basis of price fluctuations, and where selling is best option when the vast majority of investors tend to purchase goods or services, and vice versa. The players who end up being on the minority side win.The above applications of physical methods in economics are deeply rooted in classical physics. However, this paper aims to introduce the basic concepts of quantum mechanics to the process of economic phenomena modelling. Quantum mechanics is a theory describing the behaviour of microscopic objects and is grounded on the principle of wave-particle duality. It is assumed that quantum-scale objects at the same time exhibit both wave-like and particle-like properties. The key role in quantum mechanics is played by: (1) the Schrödinger equation describing the probability amplitude for the particle to be found in a given position and at a given time, and as (2) the Heisenberg uncertainty principle stating that certain pairs of physical properties cannot be economic applications of the Schrödinger equation as well as the Heisenberg uncertainty principle. We also try to describe the English auction by means the quantum mechanics methods.

scholarly journals Phenomenological implications of the generalized uncertainty principleThis paper was presented at the Theory CANADA 4 conference, held at Centre de recherches mathématiques, Montréal, Québec, Canada on 4–7 June 2008.

2009 ◽  
Vol 87 (3) ◽  
pp. 233-240 ◽  
Author(s):  
Saurya Das ◽  
Elias C. Vagenas
Keyword(s):  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Landau Levels ◽  
Quantum Mechanical ◽  
Reflection And Transmission ◽  
Heisenberg Uncertainty Principle ◽  
Transmission Coefficients ◽  
Heisenberg Uncertainty ◽  
Planck Energy

Various theories of quantum gravity argue that near the Planck scale, the Heisenberg uncertainty principle should be replaced by the so called generalized uncertainty principle (GUP). We show that the GUP gives rise to two additional terms in any quantum mechanical Hamiltonian, proportional to βp4 and β2p6, respectively, where β ∼ 1/(MPlc)2 is the GUP parameter. These terms become important at or above the Planck energy. Considering only the first of these and treating it as a perturbation, we show that the GUP affects the Lamb shift, Landau levels, reflection and transmission coefficients of a potential step and potential barrier, and the current in a scanning tunnel microscope (STM). Although these are too small to be measurable at present, we speculate on the possibility of extracting measurable predictions in the future.

scholarly journals Non-Stationary States in Physics and Biophysics

2020 ◽  
pp. 61-67
Author(s):  
Б. Г. Заславский ◽  
М. А. Филатов ◽  
В. В. Еськов ◽  
Е. А. Манина
Keyword(s):  
Quantum Mechanics ◽  
Quantum Entanglement ◽  
Uncertainty Principle ◽  
Stationary States ◽  
Unstable Systems ◽  
Heisenberg Uncertainty Principle ◽  
Human Habitat ◽  
Heisenberg Uncertainty ◽  
Self Organizing

Необходимость изучения неустойчивых систем подчеркивал I. R. Prigogine, но за последние 40 лет эта проблема не рассматривается в науке. Однако за последние 25 лет была доказана статистическая неустойчивость параметров движения в биомеханике в виде эффекта Еськова–Зинченко. Подобные неустойчивые системы имеются и в неживой природе на Земле в виде систем регуляции климата и метеопараметров среды обитания человека. Эти системы в 1948 г. W. Weaver обозначил как системы третьего типа, они обладают особой статистической неустойчивостью, характерной для самоорганизующихся систем. В работе представлены основные свойства таких систем третьего типа и некоторые инварианты для их описания. Существенно, что их моделирование основано на ряде принципов квантовой механики. В частности, принципе неопределенности Гейзенберга и квантовой запутанности. I. R. Prigogine emphasized the need to research unstable systems. However, for the last 40 years, this problem has not been studied well. Still, in the last 25 years, the statistical instability of biomechanical motion properties was proved as the Eskov–Zinchenko effect. Such unstable systems exist in the Earth’s inorganic nature, too, as the human habitat climate/weather regulation systems. In 1948 W. Weather called such systems “3rd kind systems”. They feature a special statistical instability peculiar to self-organizing systems. The study presents the key properties of such 3rd kind systems and some invariants that define these non-stationary systems. Significantly, the simulation is based on some quantum mechanics postulates. Particularly, these are the Heisenberg uncertainty principle, and the quantum entanglement principle.

scholarly journals IRROTATIONAL MOMENTUM FLUCTUATIONS CONDITIONING THE QUANTUM NATURE OF PHYSICAL PROCESSES

2006 ◽  
Vol 21 (26) ◽  
pp. 5299-5316
Author(s):  
STEPHAN I. TZENOV
Keyword(s):  
Quantum Mechanics ◽  
Statistical Mechanics ◽  
Correspondence Principle ◽  
Quantum Mechanical ◽  
Physical Processes ◽  
Expectation Values ◽  
Heisenberg Uncertainty Principle ◽  
Quantum Formalism ◽  
Classical Statistical Mechanics ◽  
Heisenberg Uncertainty

Starting from a simple classical framework and employing some stochastic concepts, the basic ingredients of the quantum formalism are recovered. It has been shown that the traditional axiomatic structure of quantum mechanics can be rebuilt, so that the quantum mechanical framework resembles to a large extent that of the classical statistical mechanics and hydrodynamics. The main assumption used here is the existence of a random irrotational component in the classical momentum. Various basic elements of the quantum formalism (calculation of expectation values, the Heisenberg uncertainty principle, the correspondence principle) are recovered by applying traditional techniques, borrowed from classical statistical mechanics.

scholarly journals Re-thinking the Foundation of Physics and its Relation to Quantum Gravity and Quantum Probabilities: Unification of Gravity and Quantum Mechanics

2020 ◽  
Author(s):  
Espen Haug
Keyword(s):  
Quantum Mechanics ◽  
Uncertainty Principle ◽  
Rest Mass ◽  
Heisenberg Uncertainty Principle ◽  
Planck Mass ◽  
Mass Particle ◽  
Modern Physics ◽  
Heisenberg Uncertainty ◽  
Derivatives Of ◽  
Mass Definition

In this paper we will show that standard physics to a large degree consists of derivatives of a deeper reality. This means standard physics is both overly complex and also incomplete. Modern physics has typically started from working with first understanding the surface of the world, that is typically the macroscopic world, and then forming theories about the atomic and subatomic world. And we did not have much of a choice, as the subatomic world is very hard to observe directly, if not impossible to observe directly at the deepest level. Despite the enormous success of modern physics, it is therefore no big surprise that we at some point have possibly taken a step in the wrong direction. We will claim that one such step came when one thought that the de Broglie wavelength represented a real matter wavelength. We will claim that the Compton wavelength is the real matter wavelength. Based on such a view we will see that many equations in modern physics are only derivatives of much simpler relations. Second, we will claim that in today’s physics one uses two different mass definitions, one mass definition that is complete or at least more complete, embedded in gravity equations without being aware of it, as it is concealed in GM, and the standard, but incomplete, kg mass definition in non-gravitational physics. First, when this is understood, and one uses the more complete mass definition that is embedded in gravity physics, not only in gravity physics, but in all of physics, then one has a chance to unify gravity and quantum mechanics. Our new theory shows that most physical phenomena when observed over a very short timescale are probabilistic for masses smaller than a Planck mass and dominated by determinism at or above Planck mass size. Our findings have many implications. For example, we show that the Heisenberg uncertainty principle is rooted in a foundation not valid for rest-mass particles, so the Heisenberg uncertainty principle can say nothing about rest-masses. When re-formulated based on a foundation compatible with a new momentum that is also compatible with rest-masses, we obtain a re-defined Heisenberg principle that seems to become a certainty principle in the special case of a Planck mass particle. Furthermore, we show that the Planck mass particle is linked to gravity and that we can easily detect the Planck scale from gravity observations. The Planck mass particle is unique as it only lasts the Planck time, and in that very short time period it can only be observed directly from itself, and it therefore closely linked to absolute rest.

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